Companies involved in, for example, oil exploration use seismic prospecting techniques to model the earth's interior with a view towards locating areas likely to contain oil before expending large amounts in drilling. In seismic prospecting over a particular area, a source of sound energy and receivers are arrayed over the area in a selected arrangement. The source transmits pulses of sound energy at the earth and the receivers receive energy which is reflected due to subsurface structural features, such as discontinuities between diverse rock and other formations. Typically, the operations are repeated a number of times with diverse arrangements of source and receivers over the area. The pattern of time delays between the transmission by the source and reception at the various receivers for the various source/receiver arrangements provides information as to the subsurface structure. If a test area, that is, the area whose subsurface structure is being investigated, has a subsurface structure which is similar to the subsurface structure of areas which are known to have oil, the likelihood that the test area also has oil is enhanced. Thus, knowledge of the subsurface structure can operate as a guide to areas where test drilling may be worthwhile.
As a more specific example, in modelling the interior of the earth under a body of water such as an ocean, typically an exploration vessel pulls a sound source and a plurality of equally-spaced receivers forming a linear array floating on the surface of the water. At a particular point of the area to be modelled, the source transmits a sound pulse directed toward the ocean floor. As the pulse reaches the ocean floor, some of the pulse energy will be reflected back toward the ocean surface and part will be absorbed into the ocean floor. As the absorbed portion continues travelling downwardly under the ocean floor, it will encounter discontinuities in the subsurface structures such as sand and rock strata formations which will also partially reflect portions of the pulse's energy back toward the ocean surface. The unreflected pulse energy may continue downwardly, with portions being reflected at subsequently-encountered discontinuities, until it finally dissipates.
During such a "shot," the receivers continuously record the amplitude of received audio signals, in at least the audio-frequency band of the signals transmitted by the source, as a function of time from the transmission by the source. Generally, each receiver will record the amplitude digitally, that is, it will record the amplitude as a number whose value represents a relative amplitude level, at each of a plurality of successive time intervals from the beginning of the shot. Normally, the amplitudes, and thus the recorded numbers, will be relatively low. However, when reflected pulse energy arrives at a receiver, the signal amplitude as recorded thereby will be relatively large. The time intervals from the time the source transmits the sound energy and the times pulse energy is received by the receivers, provides information as to the depths of the discontinuity at which the pulse was partially reflected, in the area of the ocean under the receiver array. After a selected time period, which may be related to the dying-out of reflected signals or the depth from which reflected signals would be received, the linear array is then moved a selected distance in a direction along the array and the procedure repeated. The record of signal amplitudes as recorded by the receivers provides information as to the structure of the formations of sand and row strata below the ocean floor, which, in turn, may assist in locating areas where oil is likely to be found under the ocean floor. Similar operations may be performed to generate a profile of subterranean discontinuities beneath the surface of the earth on land.
In analyzing tile information accumulated by the receivers, it is normally assumed that the receivers receive the reflected signal along a signal path that is generally vertical. This assumption is generally valid for formations defined by discontinuities that are generally planar and horizontal or sloping at shallow angles, since the perpendicular to the surface of such a discontinuity is generally vertical and the path of the reflected signal is close to being parallel thereto. However, the assumption is not valid for formations defined by discontinuities at steep angles or that are curved. If the perpendicular to the surface of the discontinuity substantially deviates from the vertical, the assumption will result in the model of the discontinuity being at a significantly different angle.
Similarly, if a discontinuity is curved, the assumption will render the discontinuity as having a substantially larger or smaller effective diameter at the same depth. For example, if the sound pulse is reflected from a concave discontinuity, the receivers will effectively model the discontinuity as having a larger diameter, as a function of depth, than it actually has, with the increase in size being inversely related to the effective diameter of the discontinuity. In addition, portions of the surface of the discontinuity whose perpendiculars increasingly deviate from the vertical will be increasingly modeled as being closer to the receivers, and hence closer to the surface of the sea floor, than they actually are. Conversely, if the sound pulse is reflected from a convex discontinuity, the receivers will effectively model the discontinuity as being smaller than it actually is, and portions of the surface of the discontinuity with normals increasingly deviating from the normal will be increasingly modeled as being farther from the surface of the sea floor, than they actually are.
Several techniques have been developed to correct such deviations. In one such technique, termed "depth migration," the signal data as received by the receivers are processed to effectively simulate a situation in which the source and receivers, in a series of iterations, are step-by-step moved downwardly. In such a "downward migration" procedure, with each step the models of the discontinuities contained within the portion of the profile traversed by the step are corrected.